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Spiking neural networks, known as the third generation of artificial neural networks, are proposed for physics-based artificial intelligence. Accompanied by a new pseudo-explicit integration scheme based on spiking recurrent neural networks leading to a spike-based pseudo explicit integration scheme, the underlying differential equations are solved with a physics-informed strategy. We propose additionally a third-generation spike-based Legendre Memory Unit that handles large sequences. These third-generation networks can be implemented on the coming-of-age neuromorphic hardware resulting in less energy and memory consumption. The proposed framework, although implicit, is viewed as a pseudo-explicit scheme since it requires almost no or fewer online training steps to achieve a converged solution even for unseen loading sequences. The proposed framework is deployed in a Finite Element solver for plate structures undergoing cyclic loading and a Xylo-Av2 SynSense neuromorphic chip is used to assess its energy performance. An acceleration of more than 40% when compared to classical Finite Element Method simulations and the capability of online training is observed. We also see a reduction in energy consumption down to the thousandth order.<\/jats:p>","DOI":"10.1007\/s00366-024-01967-3","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T04:01:41Z","timestamp":1712894501000},"page":"2703-2738","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Brain-inspired spiking neural networks in Engineering Mechanics: a new physics-based self-learning framework for sustainable Finite Element analysis"],"prefix":"10.1007","volume":"40","author":[{"given":"Saurabh Balkrishna","family":"Tandale","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-2310","authenticated-orcid":false,"given":"Marcus","family":"Stoffel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"key":"1967_CR1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.4.100501","volume":"4","author":"MP Brenner","year":"2019","unstructured":"Brenner MP, Eldredge JD, Freund JB (2019) Perspective on machine learning for advancing fluid mechanics. 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